Conservation of energy
We’re really moving now—on to the conservation of energy already! Here, I derive the principle of the conservation of energy in the presence of conservative forces, introducing the concept of path dependence along the way. We then cover simple harmonic motion by finding the potential energy of a mass attached to a perfect spring and solving its equation of motion. In doing so, we figure out the mystery of why \(i\) is showing up in a mechanics problem by introducing phase space.